A specialized finite element is developed for the study of woven
composites. The element utilizes an asymptotic displacement expansion
comprised of the homogenized displacements and the local
micro-displacements associated with the woven unit-cell elasto-statics.
Basic trigonometric functions developed in an earlier work, are
employed as solutions to the
local woven unit-cell problem under a general state of in-plane loading.
The formulation also incorporates robust unit-cell geometry
models for both polymer and ceramic matrix woven systems.
As a result, the element can be used to predict not only the macroscopic
homogeneous elastic response but also the microscopic elastic response
of a finite geometry of a woven composite subjected to
a general in-plane as well as transverse bending loading.
The element performance is demonstrated by solving the finite geometry
uni-axial tension problem and via near-tip studies for a crack
under mode-I, mode-II, and mixed mode fracture conditions. In each case,
the specialized element predictions are compared to known solutions for
a corresponding cracked orthotropic material subjected to
the same macroscopic loading conditions as well as the approximate
solutions obtained using the well established
4-noded isoparametric plane elasticity element.